The ultimate goal of mathematics is to eliminate all need for intelligent thought.

A lot of the high-level sports are really in your mind.

Incidentally, when we're faced with a "prove or disprove," we're usually better off trying first to disprove with a counterexample, for two reasons: A disproof is potentially easier (we need just one counterexample); and nitpicking arouses our creative juices. Even if the given assertion is true, our search for a counterexample often leads to a proof, as soon as we see why a counterexample is impossible. Besides, it's healthy to be skeptical.

Someone has remarked that 'An ideal math talk should have one proof and one joke and they should not be the same'.

Someone has said that all the great jugglers are dead.

Math is sometimes called the science of patterns.

It wouild be very discouraging if somewhere down the line you could ask a computer if the Riemann hypothesis is correct and it said, 'Yes, it is true, but you won't be able to understand the proof.' John Horgan.